Problem 90 - Algebra and Trigonometry

Question

Explain how to divide rational expressions.

Step-by-Step Solution

Answer

To divide rational expressions, rewrite the problem in multiplication form by taking the reciprocal of the second expression. Factor the numerators and denominators, then multiply across to get the new numerator and denominator. Finally, simplify the fraction and state restrictions in the denominator.

Step 1: Write the Problem in Multiplication Form

Rewrite the division problem as a multiplication problem. This is done by taking the reciprocal of the second rational expression and changing the operation from division to multiplication.

Step 2: Factor the Numerator and Denominator

Factor the numerator and the denominator of both rational expressions, if possible. Factoring is a necessary step as it allows for simplification in the next steps.

Step 3: Multiply the Numerators and Denominators

Multiply the numerators together to get the numerator of the answer. Do the same for the denominators.

Step 4: Simplify

If possible, simplify the fraction by canceling factors that appear in both the numerator and denominator.

Step 5: State the Restrictions

After obtaining the solution, it is important to state the restrictions in the denominator. These are the values that would make the denominator zero, as division by zero is undefined.